Also, I'm not sure why you think it was a "PR" piece and so on! Reilly mocks a whole bunch of things - the ice jug being driven in its own car, the fact that the super-rich athlete never has to pay for anything...several others. Read this passage:
--
"Mr. Reilly? Kobe is going to need to leave in exactly one minute. He was mistaken as to the start of tonight's game. Can you be expedited down here immediately?"
"Uh, well, yeah, I can expedite."
--
This is mocking! He is mocking the treatment of Kobe as some president-like figure who must go places in "exactly one minute" and has minions who "expedite" acquaintances out of rooms.
"Gods do not park," moreover, was certainly not fawning! At least that's not how I read it. I read it as another tongue-in-cheek comment on the fawning world that lets guys like Kobe get away with never parking. In other words, Reilly isn't calling Kobe a god. He's channeling the yahoos on the freeway who see Kobe that way.
This, all, is why I didn't mind all the banal "I-am-nice-person, believe-me" quotes from Kobe. When writing about the utter ludicrousness of the man's existence, he has to give him a chance to explain how he's a normal person despite the ludicrousness. Even though he's almost certainly not a normal person, it was only fair.